That is the tell tale limp door handle from a broken assembly. The part you linked looks correct. Although FWIW, you can get the same part from FCP with a lifetime warranty for cheaper. Or Get the cheaper Febi (em brand) for even less which can be a bit of a gamble, but with the lifetime warranty/return policy you can end up way ahead.
https://www.fcpeuro.com/BMW-parts/X5...ds=51218243616